To expand the expression \((x+2)(x-7)\), apply the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first binomial by each term in the second binomial:

\[
(x+2)(x-7) = x(x-7) + 2(x-7)
\]

Now, distribute:

\[
= x^2 - 7x + 2x - 14
\]

Finally, combine the like terms:

\[
x^2 - 5x - 14
\]

So, the expanded form of \((x+2)(x-7)\) is:

\[
x^2 - 5x - 14
\]

Would you like further details or have any questions? Here are 5 related questions:

1. What is the factored form of \(x^2 - 5x - 14\)?
2. Can you find the roots of the equation \((x+2)(x-7) = 0\)?
3. How would you complete the square for the expression \(x^2 - 5x - 14\)?
4. How do you graph \(y = (x+2)(x-7)\) or \(y = x^2 - 5x - 14\)?
5. How does the discriminant help in solving quadratic equations like \(x^2 - 5x - 14 = 0\)?

**Tip:** Always simplify expressions by combining like terms where possible to get the cleanest form.

Learn how to expand and simplify the binomial expression (x+2)(x-7) by applying the distributive property. This problem includes key algebraic concepts such as binomial expansion, factoring, and solving quadratic equations. Suitable for students in Grades 8-10.

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